In this talk, I discuss our recent research activity in electromagnetics, nano-optics, acoustics and mechanics, showing how suitably tailored meta-atoms and suitable arrangements of them open exciting venues to realize new phenomena and devices for light, radio-waves and sound. I discuss venues to largely break Lorentz reciprocity and realize isolation without the need of magnetic bias, based on broken time-reversal symmetry induced by mechanical motion, spatio-temporal modulation and/or nonlinearities. I also discuss how broken symmetries in space and space-time can open the opportunity to induce topological order in metamaterials. Another class of interesting metamaterials based on broken symmetries are parity-time symmetric metamaterials, which are asymmetric in space, but symmetric upon parity and time inversion. In the talk, I will also discuss the impact of these concepts from basic science to practical technology, from classical waves to quantum phenomena.
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